The Art of Modeling in Science and Engineering with Mathematica

 A FIRST LOOK AT MODELING
The Physical Laws
The Rate of the Variables: Dependent and Independent Variables
The Role of Balance Space: Differential and Integral Balances
The Role of Time: Unsteady State and Steady State Balances
Information Derived from Model Solutions
Choosing a Model
Kick-Starting the Modeling Process
Solution Analysis
Practice Problems

ANALYTICAL TOOLS: THE SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
Definitions and Classifications
Boundary and Initial Conditions
Analytical Solutions of ODEs
Nonlinear Analysis
Laplace Transformation
Practice Problems

THE USE OF MATHEMATICA IN MODELING PHYSICAL SYSTEMS
Handling Algebraic Expressions
Algebraic Equations
Integration
Ordinary Differential Equations
Partial Differential Equations
Practice Problems

ELEMENTARY APPLICATIONS OF THE CONSERVATION LAWS
Application of Force Balances
Applications of Mass Balance
Simultaneous Applications of the Conservation Laws
Practice Problems

PARTIAL DIFFERENTIAL EQUATIONS: CLASSIFICATION, TYPES, AND PROPERTIES - SOME SIMPLE TRANSFORMATIONS
Properties and Classes of PDE
PDEs of Major Importance
Useful Simplifications and Transformations
PDEs PDQ: Locating Solutions in the Literature
Practice Problems

SOLUTION OF LINEAR SYSTEMS BY SUPERPOSITION METHODS
Superposition by Addition of Simple Flows: Solutions in Search of a Problem
Superposition by Multiplication: Product Solutions
Solution of Source Problems: Superposition by Integration
More Superposition by Integration: Duhamel's Integral and the Superposition of Danckwerts
Practice Problems

VECTOR CALCULUS: GENERALIZED TRANSPORT EQUATIONS
Vector Notation and Vector Calculus
Superposition Revisited: Green's Functions and the Solution of PDEs by Green's Functions
Transport of Mass
Transport of Energy
Transport of Momentum
Practice Problems

ANALYTICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS
Separation of Variables
Laplace Transformation and Other Integral Transforms
The Method of Characteristics
Practice Problems